The present invention relates to a gradient coil manufacturing method, a gradient coil and a magnetic resonance imaging system, and particularly to a gradient coil provided on a polar surface of a static magnetic field magnet, a method of manufacturing the same, and a magnetic resonance imaging system having such a gradient coil.
In a magnetic resonance imaging (MRI: Magnetic Resonance Imaging) system, a target to be shot or imaged is carried in an internal bore of a magnet system, i.e., a bore or space in which a static magnetic field is formed. A gradient magnetic field and a high-frequency magnetic field are applied to produce a magnetic resonance signal within the target. A tomogram is produced (reconstructed) based on its received signal.
In a magnet system using permanent magnets for generating static magnetic fields, pole piece for uniformizing a magnetic flux distribution in a static magnetic field space are respectively provided at leading ends of a pair of the permanent magnets opposite to each other. Further, gradient coils for generating gradient magnetic fields are provided on their corresponding polar surfaces of the pole pieces.
In the above-described magnet system, the pole pieces are magnetized by the gradient magnetic fields since the gradient coils are respectively close to the pole pieces. Due to the residual gradient magnetic fields formed by their remanent magnetization, the phase of a spin is subjected to such an influence as though eddy currents extremely long in time constant had existed. Therefore, it would interfere with imaging made by, for example, a fast spin echo (FSE) method or the like which needs accurate phase control.
Therefore, an object of the present invention is to implement a gradient coil low in magnetizing force with respect to each pole piece, a method of manufacturing the same, and a magnetic resonance imaging system having such a gradient coil.
(1) The invention according to one aspect for solving the above problems is a gradient coil manufacturing method comprising the step of, upon manufacturing a pair of gradient coils which is respectively provided along the surfaces of bottom plate portions lying inside peripheral edge portions of a pair of pole pieces having the bottom plate portions and the peripheral edge portions protruding in the direction orthogonal to the surfaces of the bottom plate portions, the pole pieces being opposed to each other with the protruded peripheral edge portions formed with a space defined therebetween, and which produces gradient magnetic fields in the space by currents that flow through a plurality of concentric passes, setting the maximum radius of one of the passes for each of the gradient coils to the minimum value within a range for producing a gradient magnetic field having a magnetic field error lying within a predetermined allowable range.
In the invention according to this aspect, the maximum radius of one pass for each gradient coil is set to the minimum value at which a gradient magnetic field having a magnetic field error lying within a predetermined allowable range can be produced. Thus, the distance between the outermost pass and a protruded peripheral edge portion of each pole piece increases. Therefore, the magnetizing force with respect to the protruded peripheral edge portion is low and the residual magnetization is low.
(2) The invention according to another aspect for solving the above problems is the gradient coil manufacturing method described in (1), wherein the radii of the plurality of passes are determined according to the following procedures.
Note
(a) setting measurement points Pi (where i=1xe2x88x92N) onto the maximum spherical surface supposed in an imaging area.
(b) calculating magnetic fields Bit (where i=1xe2x88x92N) at the measurement points, to be produced by the gradient coils.
(c) setting a tolerance at for an error with respect to each magnetic field.
(d) setting an allowable value r0 of the maximum radius of the pass for each gradient coil within a range not exceeding a limit value r00.
(e) defining the radii of the plurality of passes as r1, r2, . . . , rM.
max (r1, r2, . . . , rM) less than r0,
under the above restricted condition, and
{right arrow over (r)}=(r1, r2, . . . , rM)
with the above as a parameter,   min  ⁡      [                  ∑                  i          =          1                N            ⁢              xe2x80x83            ⁢                        {                                    B              it                        -                                                            B                  ^                                i                            ⁢                              xe2x80x83                            ⁢                              (                                  r                  ⇀                                )                                              }                2              ]  
determining the optimum values of rj (where j=1xe2x88x92M) using quadratic programming so that the above equation 18 is established. Incidentally,
{circumflex over (B)}i({right arrow over (r)})
the above is calculated using the Biot-Savart""s law.
(f) calculating an error in magnetic field at each measurement point Pi according to the following equation.       α    i    =                                                        B              ^                        i                    ⁢                      xe2x80x83                    ⁢                      (                          r              ⇀                        )                          -                  B          it                            B        it              xc3x97    100  
(g) determining rj when xcex1ixe2x89xa6xcex1t is satisfied.
(h) when xcex1ixe2x89xa6xcex1t is not satisfied, increasing the allowable value r0 within a range not exceeding the limit value r00 and (i) repeating the procedures subsequent to (e).
In the invention according to this aspect, the maximum radius of one pass for each gradient coil is set to the minimum value at which a gradient magnetic field having a magnetic field error lying within a predetermined allowable range can be produced. Thus, the distance between the outermost pass and a protruded peripheral edge portion of each pole piece increases. Therefore, the magnetizing force with respect to the protruded peripheral edge portion is low and the residual magnetization is low.
(3) The invention according to a further aspect for solving the above problems is a pair of gradient coils which is respectively provided along the surfaces of bottom plate portions lying inside peripheral edge portions of a pair of pole pieces having the bottom plate portions and the peripheral edge portions protruding in the direction orthogonal to the surfaces of the bottom plate portions, the pole pieces being opposed to each other with the protruded peripheral edge portions formed with a space defined therebetween, and which produces gradient magnetic fields in the space by currents that flow through a plurality of concentric passes, wherein the maximum radius of one of the passes for each of the gradient coils is set to the minimum value within a range for producing a gradient magnetic field having a magnetic field error lying within a predetermined allowable range.
In the invention according to this aspect, the maximum radius of one pass for each gradient coil is set to the minimum value at which a gradient magnetic field having a magnetic field error lying within a predetermined allowable range can be produced. Thus, the distance between the outermost pass and a protruded peripheral edge port of each pole piece increases. Therefore, the magnetizing force with respect to the protruded peripheral edge portion is low and the residual magnetization is low.
(4) The invention according to a still further aspect for solving the above problems is the pair of gradient coils described in (3), wherein the plurality of passes respectively have radii determined according to the following procedures.
Note
(a) setting measurement points Pi (where i=1xe2x88x92N) onto the maximum spherical surface supposed in an imaging area.
(b) calculating magnetic fields Bit (where i=1xe2x88x92N) at the measurement points, to be produced by the gradient coils.
(c) setting a tolerance xcex1t for an error with respect to each magnetic field.
(d) setting an allowable value r0 of the maximum radius of the pass for each gradient coil within a range not exceeding a limit value r00.
(e) defining the radii of the plurality of passes as r1, r2, . . . , rM.
max (r1, r2, . . . , rM) less than r0,
under the above restricted condition, and
{right arrow over (r)}=(r1, r2, . . . , rM)
with the above as a parameter,   min  ⁡      [                  ∑                  i          =          1                N            ⁢              xe2x80x83            ⁢                        {                                    B              it                        -                                                            B                  ^                                i                            ⁢                              xe2x80x83                            ⁢                              (                                  r                  ⇀                                )                                              }                2              ]  
determining the optimum values of rj (where j=1xe2x88x92M) using quadratic programming so that the above equation 23 is established. Incidentally,
{circumflex over (Bi)}i({right arrow over (r)})
the above is calculated using the Biot-Savart""s law.
(f) calculating an error in magnetic field at each measurement point Pi according to the following equation.       α    i    =                                                        B              ^                        i                    ⁢                      xe2x80x83                    ⁢                      (                          r              ⇀                        )                          -                  B          it                            B        it              xc3x97    100  
(g) determining rj when xcex1ixe2x89xa6xcex1t is satisfied.
(h) when xcex1ixe2x89xa6xcex1t is not satisfied, increasing the allowable value r0 within a range not exceeding the limit value r00, and (i) repeating the procedures subsequent to (e).
In the invention according to this aspect, the maximum radius of one pass for each gradient coil is set to the minimum value at which a gradient magnetic field having a magnetic field error lying within a predetermined allowable range can be produced. Thus, the distance between the outermost pass and a protruded peripheral edge portion of each pole piece increases. Therefore, the magnetizing force with respect to the protruded peripheral edge portion is low and the residual magnetization is low.
(5) The invention according to a still further aspect for solving the above problems is a magnetic resonance imaging system for forming an image based on magnetic resonance signals acquired using a static magnetic filed, a gradient magnetic field and a high-frequency magnetic field, comprising, a pair of gradient coils configured as gradient coils each of which generates the high-frequency magnetic field, the pair of gradient coils being respectively provided along the surfaces of bottom plate portions lying inside peripheral edge portions of a pair of pole pieces having the bottom plate portions and the peripheral edge portions protruding in the direction orthogonal to the surfaces of the bottom plate portions, the pole pieces being opposed to each other with the protruded peripheral edge portions formed with a space defined therebetween, and which produces gradient magnetic fields in the space by currents that flow through a plurality of concentric passes, and wherein the maximum radius of the pass is set to the minimum value within a range for producing a gradient magnetic field having a magnetic field error lying within a predetermined allowable range.
In the invention according to this aspect, the maximum radius of one pass for each gradient coil is set to the minimum value at which a gradient magnetic field having a magnetic field error lying within a predetermined allowable range can be produced. Thus, the distance between the outermost pass and a protruded peripheral edge portion of each pole piece increases. Therefore, the magnetizing force with respect to the protruded peripheral edge portion is low and the residual magnetization is low. Thus, imaging on which the residual magnetization has a little effect, can be carried out.
(6) The invention according to a still further aspect for solving the above problems is the magnetic resonance imaging system described in (5), wherein the plurality of passes respectively have radii determined according to the following procedures.
Note
(a) setting measurement points Pi (where i=1xe2x88x92N) onto the maximum spherical surface supposed in an imaging area.
(b) calculating magnetic fields Bit (where i=1xe2x88x92N) at the measurement points, to be produced by the gradient coils.
(c) setting a tolerance at for an error with respect to each magnetic field.
(d) setting an allowable value r0 of the maximum radius of the pass for each gradient coil within a range not exceeding a limit value r00.
(e) defining the radii of the plurality of passes as r1, r2, . . . , rM.
max (r1, r2, . . . , rM) less than r0,
under the above restricted condition, and
{right arrow over (r)}=(r1, r2, . . . , rM)
with the above as a parameter,   min  ⁡      [                  ∑                  i          =          1                N            ⁢              xe2x80x83            ⁢                        {                                    B              it                        -                                                            B                  ^                                i                            ⁢                              xe2x80x83                            ⁢                              (                                  r                  ⇀                                )                                              }                2              ]  
determining the optimum values of rj (where j=1xe2x88x92M) using quadratic programming so that the above equation 28 is established. Incidentally,
{circumflex over (B)}l({right arrow over (r)})
the above is calculated using the Biot-Savart""s law.
(f) calculating an error in magnetic field at each measurement point Pi according to the following equation.       α    i    =                                                        B              ^                        i                    ⁢                      xe2x80x83                    ⁢                      (                          r              ⇀                        )                          -                  B          it                            B        it              xc3x97    100  
(g) determining rj when xcex1i less than xcex1t is satisfied.
(h) when xcex1i less than xcex1t is not satisfied, increasing the allowable value r0 within a range not exceeding the limit value r00, and (i) repeating the procedures subsequent to (e).
In the invention according to this aspect, the maximum radius of one pass for each gradient coil is set to the minimum value at which a gradient magnetic field having a magnetic field error lying within a predetermined allowable range can be produced. Thus, the distance between the outermost pass and a protruded peripheral edge portion of each pole piece increases. Therefore, the magnetizing force with respect to the protruded peripheral edge portion is low and the residual magnetization is low. Thus, imaging on which the residual magnetization has a little effect, can be carried out.
According to the present invention, a gradient coil reduced in magnetizing force with respect to a pole piece, a manufacturing method therefor, and a magnetic resonance imaging system having such a gradient coil can be implemented.